A210992 Square array read by antidiagonals, in which column k starts with k plateaus of lengths k+1, k, k-1, k-2, k-3,..2 and of levels A000124: 1, 2, 4, 7, 11..., if k >= 1, connected by consecutive integers. After the last plateau the length remains 1.

1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 5, 3, 1, 1, 1, 6, 4, 2, 1, 1, 1, 7, 5, 2, 1, 1, 1, 1, 8, 6, 3, 2, 1, 1, 1, 1, 9, 7, 4, 2, 1, 1, 1, 1, 1, 10, 8, 5, 2, 2, 1, 1, 1, 1, 1, 11, 9, 6, 3, 2, 1, 1, 1, 1, 1, 1, 12, 10, 7, 4, 2, 2, 1, 1, 1, 1, 1, 1, 13, 11, 8, 4, 2, 2

Offset: 0

Author

Omar E. Pol, Jun 30 2012

Keywords

• nonn
• tabl

Comments

Column k contains k plateaus whose levels are the first k terms of A000124, therefore A000124(i) is the level of the i-th plateau of the column k when k -> infinity.

Column k contains the integers s>=1 repeated f(s) times, sorted, where f(s)=1 if s is not in A000124, otherwise, if A000124(c)=s, repeated f(s)=max(1,k+1-c) times. - R. J. Mathar, Jul 22 2012

It appears that this array can be represented by a structure in which the number of relevant nodes give A000005 (see also A210959). - Omar E. Pol, Jul 24 2012

Examples

			Illustration of initial terms of the 4th column:
------------------------------------------------------
Level    Graphic
------------------------------------------------------
10                                              *
9                                             *
8                                           *
7                                       * *
6                                     *
5                                   *
4                             * * *
3                           *
2                   * * * *
1         * * * * *
0
-------------------------------------------------------
Column 4: 1,1,1,1,1,2,2,2,2,3,4,4,4,5,6,7,7,8,9,10,...
-------------------------------------------------------
Array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
2, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
3, 2, 1, 1, 1, 1, 1, 1, 1, 1,...
4, 3, 2, 1, 1, 1, 1, 1, 1, 1,...
5, 4, 2, 2, 1, 1, 1, 1, 1, 1,...
6, 5, 3, 2, 2, 1, 1, 1, 1, 1,...
7, 6, 4, 2, 2, 2, 1, 1, 1, 1,...
8, 7, 5, 3, 2, 2, 2, 1, 1, 1,...
9, 8, 6, 4, 2, 2, 2, 2, 1, 1,...
		

Links

• Omar E. Pol, Illustration of initial terms of the columns 0..10

Crossrefs

Columns 0-1: A000027, A028310.

Cf. A000124, A195825, A210843, A210959, A211970.

Programs

Maple

A000124i := proc(n)
    local j;
    for j from 0 do
        if A000124(j) = n then
            return j;
        elif A000124(j) > n then
            return -1 ;
        end if;
    end do:
end proc:
A210992 := proc(n,k)
    local f,r,a,c;
    f := k+1  ;
    a := 1 ;
    for r from 0 to n do
        if f > 0 then
            f := f-1;
        else
            a := a+1 ;
            c := A000124i(a) ;
            f := 0 ;
            if c >= 0 then
                f := max(0,k-c) ;
            end if;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Jul 22 2012